Python Pandas how to multiply by the previous value of a string when calculating in another formula

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I have a Csv file with a calculation that looks something like this:

Average Value
2
5
9
20
3
2
4

I want to make a calculation in a new column using the formula "Y = (2/(N+1))*X+(1-(2/(N+1)))*Y1 "

Where N is the period that is given when calling the class. Here N will be 10

X = Average Value

Y1 = previous calculation of Y

I was doing something like

df['Y'] = ((2//(N + 1))*df.Average Value + (1-(2//(N + 1)))).cumsum().fillna(0)

But it doesn't work

Desired result

Average Value Y
2 1.18
5 1.84
9 3.14
20 6.20
3 5.61
2 4.95
4 4.77
pandas python
1 Answers

Numba solution - is possible count by previous values:

from numba import jit

@jit(nopython=True)
def f(a, N):
    x = (2/(N + 1))
    y = 1-(2/(N + 1))
    d = np.empty(a.shape)
    d[0] = a[0] * x + y
    for i in range(1, a.shape[0]):
        d[i] = a[i] * x + d[i-1] * y 
    return d

df['Y'] = f(df['Average Value'].to_numpy(), 10)
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